The movie, starring Tom Cruise as Ethan Hunt, will resume shooting on June 14.
A train crash scene is to be filmed at the former Darlton Quarry in Stoney Middleton.
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In a statement, Paramount Pictures said: “We have temporarily halted production on Mission Impossible 7 until June 14 due to positive coronavirus test results during routine testing.
“We are following all safety protocols and will continue to monitor the situation.”
It is not known how many people have tested positive for the disease.
In December, an audio recording released by The Sun newspaper appeared to show Mr Cruise, 58, shouting and swearing at a film crew, warning them to keep 2m away from one other.
“I don't ever want to see it again, ever!” he could be heard shouting.
“And if you don't do it, you're fired.
“If I see you do it again, you're gone.
“And if anyone in this crew does it - that’s it, and you too and you too… don’t you ever do it again.”
"That’s it! No apologies,” he continued.
“You can tell it to the people that are losing their homes because our industry is shut down.
“It’s not going to put food on their table or pay for their college education.”
The seventh instalment of the Mission Impossible franchise, directed by Christopher McQuarrie, is belatedly set for release next May and will also feature actors Simon Pegg, Ving Rhames and Vanessa Kirby, along with Rebecca Ferguson and Henry Czerny.